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Georg Cantor :Life and Accomplishments

Georg Cantor :Life and Accomplishments. Erick Gonzalez Juan Favela Jacob Bautista. Life/ Leben. Georg Ferdinand Ludwig Philipp Cantor March 3, 1845 Valley Oldest of 6 children Baptized as Lutherans & devoted Christian 3 0ut of 20 letter books Bacon/ Shakespear

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Georg Cantor :Life and Accomplishments

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  1. Georg Cantor:Life and Accomplishments Erick Gonzalez Juan Favela Jacob Bautista

  2. Life/Leben • Georg Ferdinand Ludwig Philipp Cantor • March 3, 1845 • Valley • Oldest of 6 children • Baptized as Lutherans & devoted Christian • 3 0ut of 20 letter books • Bacon/Shakespear • the Realschule in Darmstadt, the Federal Polytechnic Institute, University of Berlin

  3. Probleme des Unendlichen: Werk und Leben Georg Cantors (1967) • Beitrage (of 1895 & 1897) • 1862 devoted his life to Math • Leopold Kronecker, continuum hypothesis • 1896 mother, 3 years later brother • Artist

  4. 1-to-1 • Correspondence between line segment and unit square • “for any positive integer n, there exists a 1-to-1 correspondence between the points in an n-dimensional space.” 1 -> A 2 -> B 3 -> C 4 -> D

  5. The Set Theory • Branch of Math was in an article called ("On a Property of the Collection of All Real Algebraic Numbers").[ • Proved that real numbers and positive integers are not equinumerous.

  6. Continuum Hypothesis • Created in 1877 about the possible sizes of infinite sets • “There is no set whose cardinality is strictly between that of the integers and that of the real numbers.”

  7. Cont. • First stated “the cardinality of the set of integers is strictly smaller than that of the set of real numbers” • Cantor’s First Uncountability Proof and Cantor’s Diagonal Argument • Hypothesis proves the extent of the cardinality

  8. Death • Nervous Breakdowns • Heart Failure • Died January 6, 1918

  9. References • Dauben, Joseph Warren. 1979 “Georg Cantor, His Mathematics and Philosophy of the Infinite” Ch. 1 Pg. 1-5, Ch.6 Pg. 120-148 • Everdell, William R. “The First Moderns”. 1997 • http://en.wikipedia.org/wiki/Georg_Cantor

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